Gray Level Transformation to Increase the Density of Interferometric Fringes

A gray level transformation is presented to simulate the interferometric process. The transformation uses properties of sinusoidal functions to produce rapidly varying intensities from those with nearly zero gradients. The transformation when used in conjunction with optical techniques, such as holographic interferometry, has the effect of increasing the optical sensitivity and producing a large number of fringes where otherwise only a fraction of a fringe would be observed. This technique is ideal for holographic analysis of deformations in microscopic regions.

I. Introduction

Optical techniques such as holographic interferometry are utilized as extremely sensitive and accurate full field methods to determine displacements and strains.^1,2 Numerous signal processing techniques have been developed to retrieve phase information from interferometric fringe patterns.^3,4 As in the case of double exposure holography, once the fringes are formed and recorded on the holographic medium, be it emulsion or thermoplastic type, the recorded image is then routed to an image digitizer via a video camera where it is digitized and stored in a frame buffer for further analysis.

The deformations producing the fringe pattern together with the sensitivity of the optical setup are ordinarily large enough to generate many fringes in the field of analysis. One of the most difficult and seemingly unresolved aspects of accurate determination of deformations, however, occurs when the phase variation in the field of analysis is less than a complete cycle. This is because, in almost all circumstances, extraction of phase information from signals (be it analog or digital) containing low frequency components is subject to large errors. This problem was studied thoroughlyinRef.5,and it was determined that its solution requires generating an auxiliary system of carrier fringes by optical means, and thus shifting the phase information to a higher frequency, that of the carrier fringes. The small perturbations of the phase of the carrier fringes can now be accurately detected by the use of FIR linear phase filters⁶ and the appropriate techniques such as those outlined in Ref. 5.

In the present work we discuss a gray level transformation that can be applied to the recorded intensity variation that mimics the formation of fringes in optical processes. The transformation can be implemented on an image processor as the first stage of image acquisition, provided that the recorded holographic interferometric intensity has been optically filtered so that it does not contain a speckle pattern. If, however, the fringe pattern suffers from random intensity variation of speckle, the transformation can be applied in the second stage of image acquisition, after the fringe pattern has been numerically filtered.

It should be noted that, although the transformation is intended to be applied on interferometric images, it is not limited to them. It can be used to detect minute intensity changes, both qualitatively and quantitatively,since, as is shown, the transformed images are sinusoidal in form and numerous signal processing algorithms have been developed to process these types of image.

II. Formation of Holographic Interferometric Fringes

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